$2$ Signal Timing $[25$ points$]$

For the geometric and traffic characteristics shown below, determine a suitable signal phasing system

and phase lengths for the intersection using Webster method. Show a detailed layout of the phasing

system and intersection geometry used. Additionally, calculate the critical $\frac{v}{c}$ ratio $x_c$ for the

intersection. Assume travel lanes between $9-12$ ft and a PHF of $0\mathrm{.}95.$

Peak Hour Volumes:

Assume the following saturation flows:

Through lanes: $1600ve\frac{h}{h}\frac{r}{l}$ane

Through$-$right lanes: $1400ve\frac{h}{h}\frac{r}{?}$ lane

Exclusive left turn: $1500ve\frac{h}{h}\frac{r}{l}$ane

Left lanes: $1000ve\frac{h}{h}\frac{r}{?}$ lane

Left$-$through lanes: $1200ve\frac{h}{h}\frac{r}{?}$ lane

Left$-$through$-$right lanes: $1100ve\frac{h}{h}\frac{r}{?}$ lane